Abstract: Methods, apparatuses, and computer readable media for location measurement reporting in a wireless network are disclosed. An apparatus of an initiator station (ISTA), where the apparatus comprises processing circuitry configured to encode a null data packet announce (NDPA) frame for transmission to a responder station (RSTA), the NDPA frame indicating a sounding sequence number, and encode a first null data packet (NDP) for transmission at a time T1 to the RSTA. The processing circuitry may be further configured to: decode a second NDP, the second NDP received from the RSTA, wherein the second NDP is received at a time T4, and decode a first location measurement report (LMR). The processing circuitry may be further configured to in response to an ISTA-to-RSTA LMR feedback agreement between the RSTA and ISTA indicating the ISTA is to send a second LMR, encode a second LMR.

Abstract: A method and apparatus are provided to determine a range of a sling load from a vehicle. In one embodiment, an FMCW RADAR altimeter generates an altitude history image that is used to determine the range of the sling load from the vehicle and an altitude of the vehicle.

Abstract: Methods, systems, and apparatus for transmitting a first set of continuous wave (CW) signals, where each CW signal of the first set of CW signals has a first signal frequency and the transmitter is turned off between transmission of each CW signal of the first set of CW signals. For each CW signal of the first set of CW signals, receiving a reflection of the CW signal, and selecting an analog to digital (A/D) sample of the reflection of the CW signal that does not contain ground reflections by selecting the A/D sample based on timing from the transmitter being turned off after transmission of the CW signal. Integrating the selected A/D samples from each of the CW signals of the first set of CW signals to obtain a single A/D sample for the first set of CW signals.

Abstract: A system for determining the position of a transmitting unit has an arrangement of at least four transmitting units. A first transmitting unit is designed to emit a first transmission signal to each of the three remaining units, each of which is designed to receive the first transmission signal and, thereafter, to return a first response signal to the first unit. The three remaining units each have stored position data relating to desired positions of the arrangement. The first unit is designed to: determine its relative position data relative to the three remaining units based on the returned first response signals, obtain the stored position data relating to the desired positions from the three remaining units, and assign the determined relative position data to the obtained position data relating to a single desired position to determine the position of the first unit within the arrangement based on the assignment.

Abstract: A method and apparatus for side vehicle positioning are provided for positioning a side vehicle accurately. The method includes: converting an original image into an corrected image, the original image being an image shot by an image acquisition device, the corrected image being an image corresponding to the original image under an angle of view of a virtual camera; detecting a wheel feature in a detection region of the corrected image, and acquiring a position of a subimage including the wheel feature in the corrected image; detecting a circle feature in the subimage including the wheel feature, and acquiring a circle detection result, the circle detection result including a position of a circle center of the circle feature in the corrected image and a radius of the circle feature; and acquiring side vehicle positioning information according to the circle detection result.

Abstract: A system includes an automotive-based processor configured to receive a road-scanning instruction. The processor is further configured to instruct a vehicle-mounted sonar to scan an upcoming section of terrain and receive scan data from the sonar, responsive to the instruction. The processor is additionally configured to convert the scan data to a visual display showing at least obstacles and elevations and present the visual display on an in-vehicle display.

Abstract: There is provided a distance measurement device that can successfully take in reflected light from a distance measurement area, and at the same time, can achieve compactness of the distance measurement device. The distance measurement device includes a fixed part, a rotating part that is rotatably disposed on the fixed part, a laser light source that is disposed in the fixed part, and a photodetector that is disposed in the fixed part. The distance measurement device further includes a beam splitter that is disposed in the fixed part and separates an optical path of projection light emitted from the laser light source from an optical path of reflected light reflected by a distance measurement area and an imaging lens that is disposed in a common optical path of projection light and reflected light and is used for taking in reflected light reflected by the distance measurement area.

Abstract: A distance detector comprising: a laser transmitter and receiver for generating a laser beam to irradiate an object and to receive return light reflected in response from the object, an image detection system for generating an image of a view, the image detection system including an objective lens for collecting light from the view, an image sensor for receiving light collected by the objective lens and for generating the image therefrom, and a digital display for displaying the image such that the digital display displays a real-time image of the view, a laser beam indicium on the digital display or a laser beam indicium generator configured to display laser beam indicium on the digital display, wherein the laser beam indicium indicates a direction of the laser beam, and a range-finding system for determining the distance to an object irradiated by the laser beam using return light and for displaying distance.

Abstract: An object detection apparatus includes: a light emitting unit; a light receiving unit; an object detection unit; a lightness and darkness determination unit that determines an ambient state of lightness or darkness; a signal amplification unit that sets an amplification ratio for a light reception signal and causes the light reception signal to be output from the light receiving unit at a level in accordance with the amplification ratio; and an amplification control unit that controls the amplification ratio for the light reception signal. The amplification control unit causes an amplification ratio for the light reception signal in a case where the lightness and darkness determination unit determines that the ambient state is dark to be higher than an amplification ratio for the light reception signal in a case where the lightness and darkness determination unit determines that the ambient state is light.

Abstract: An optical device creates a 3D image of a volume of interest comprising horizontal, vertical, and distance information for each voxel. Two pairs of two Risley prisms rotate synchronously to first create outgoing modulated illumination beams, and second to direct incoming light to an image sensor. Synchronization allows the imaging portion of the system to look at the same field of view as is illuminated. This field of view is smaller than the volume of interest. The field of view is scanned both horizontal and vertically to encompass the volume of interest, and may by directed to any arbitrary field of view. The illumination beam is amplitude modulated. The image sensor demodulates synchronously, computing time-of-flight for each pixel. Modulation frequency and sensor integration time are dynamically adjusted responsive to a desired volume of interest or field of view.

Abstract: An optical device creates a 3D image of a volume of interest comprising horizontal, vertical, and distance information for each voxel. An illumination beam director and an imaging beam director are synchronized to each point to a selected, arbitrary, dynamically selectable reduced field of view, within a total field of view. Each reduced field of view is illuminated at once by a modulated continuous wave light source; and is imaged at once, using a pixel-array image sensor comprising time-of-flight for each of at least 8,000 pixels. The device sequences through 4 to 600 reduced fields of view until the total field of view is imaged. The device is free of rotating mechanical components. The pixel-array image sensor demodulates synchronously with the light source. Modulation frequency and sensor integration time are dynamically adjusted responsive to a desired volume of interest or field of view.

Abstract: A LIDAR system which includes a laser radiation source for generating coherent laser radiation, the LIDAR system being designed for emitting the laser radiation emitted by the LIDAR system essentially in propagation modes which correspond to analytical solutions of the paraxial Helmholtz equation including two ordinal numbers, at least one of the two ordinal numbers being greater than 0.

Abstract: A light beam scanning device includes a lens element assembly which dynamically adjusts a divergence of the beam. The lens element assembly can include multiple lens elements, one or more of which translates parallel to the light beam to adjust beam divergence. Divergence adjustment can include adjusting the beam divergence along one or more cross sectional axes of the beam. Beam divergence can be adjusted between consecutive scans, during a scan, etc. Beam divergence can be adjusted based on the field of view and scan rate. Beam divergence adjustment can enable dynamic adjustment of the spot size of the beam, which can enable the apparatus to adjust between scanning a wide divergence beam to detect objects in a scene and scanning a narrow divergence beam to generate detailed point clouds of the detected objects. Beam divergence adjustment can enable adjustment of reflection point intensity, enabling detection of low-reflectivity objects.

Abstract: The present application generally relates communications and hazard avoidance within a monitored driving environment. More specifically, the application teaches a system for improved target object detection in a vehicle equipped with a laser detection and ranging LIDAR system by simultaneously transmitting multiple lasers in an array and resolving angular ambiguities using a plurality of horizontal detectors and a plurality of vertical detectors.

Abstract: An advanced map DB 43 stored on a server device 4 includes pulse type information that is configuration information for detecting a landmark using a LIDAR 2. By sending request information D1 including own vehicle position information, the vehicle mounted device 1 receives response information D2 including pulse type information corresponding to a landmark around the own vehicle position and controls the LIDAR 2 on the basis of the received pulse type information.

Abstract: A system for measuring velocity of particles such as particles in air is a Light Detection and Ranging (LIDAR) system, having a micro-electro-mechanical-system (MEMS).

Abstract: A spectrally-resolved Raman water lidar, including: a transmitter unit, a receiver unit, and a data acquisition and control unit. The transmitter unit includes a seeder, a solid Neodymium-doped Yttrium Aluminum Garnet (Nd: YAG) laser, a beam expander, and a first reflecting mirror to emit a 354.8-nm laser beam. The receiver unit includes a telescope, an iris, a collimator, a second reflecting mirror, a first bandpass filter, a beam splitter, a narrow-band interference filter, a third lens, a first detector, a second bandpass filter, a coupler and a home-made dual-grating polychromator to enable simultaneous profiling of backscattered Raman spectrum signals from water vapor, water droplets and ice crystals as well as aerosol fluorescence in the atmosphere. The data acquisition and control unit includes a computer to store the acquired data and guarantee an automatic operation of the lidar system through a time-sequence circuit.

Abstract: Various aspects of the disclosure relate to managing ephemeris information. Provisions are made for providing ephemeris information to a user terminal (UT). Messages are defined for sending ephemeris information and for requesting ephemeris information. Ephemeris information for a subset of the satellites in a constellation may be sent to a UT to reduce signaling load. A UT may manage a database of ephemeris information to ensure freshness of the ephemeris information.

Abstract: A navigation system that utilizes a discrete-time nonlinear filter to obtain a navigation solution using GPS signals and optional aiding sensor data is described. A nonlinear filter offers improved accuracy over linearized filters at low signal to noise ratios. A discrete-time nonlinear filter guarantees positive-definite calculated covariance matrices under all conditions without requiring any compensation or added parameters. The navigation system receives a modernized global navigation satellite system (GNSS) signal and correlates a digitized copy of the GNSS signal to generate flinging code measurements. A conditional probability density function for the code measurements is determined and used to calculate arbitrary moments of code delay and other expected values.

Abstract: A Global Navigation Satellite System receiver for position determination receives from a multitude of satellites a respective GNSS code signal, which are correlated with a reference code signal to obtain an autocorrelation function. A multitude of function values of the autocorrelation function at different discrete chip spacings (chosen asymmetrically with respect to a prompt chip spacing) are analyzed and used in obtaining a test metric. Using the test metric, a decision is made whether the received GNSS code signal is suitable or unsuitable (thereafter excluded) for a position determination due to multipath signal components. A bias removal is performed taking into account corresponding function values of an autocorrelation function that would result from a received GNSS code signal of the satellite unaffected by multipath signal components. This provides a simple method for operating a GNSS receiver minimizing errors in position determination caused by multipath signal components.

Abstract: A positioning position is corrected more efficiently. A reception control device, comprising: a processor, wherein the processor executes: a reception parameter acquisition process of acquiring reception parameters related to reception of positioning signals from a positioning signal receiver that receives the positioning signals from positioning satellites; a first reception environment determination process of determining a reception environment on the basis of a result of determining the acquired reception parameters in accordance with determination conditions; and a reception control process of controlling an error correction signal receiver that receives an error correction signal for correcting an error of a positioning result by the positioning signals from an error correction satellite on the basis of a determination result in the first reception environment determination process.

Abstract: A universal multi-channel receiver for receiving and processing signals from different navigation systems is provided. The universal receiver is implemented as an ASIC receiver with a number of universal channels. The receiver with universal channels is capable of receiving and processing signals from navigation satellites located within a direct access zone. The universal receiver has a plurality of channels that share the same memory. The universal receiver can determine its coordinates using any of the existing navigation systems (GPS, GLONASS, Beidou and GALILEO). The receiver can receive and process any (PN) signals.

Abstract: A mesh network localization system includes at least one base station located on a building roof to receive a GPS signal from a satellite and to transmit a base station location signal. An infrastructure device is located at a ground level to derive its global position based on the base station location signal. A mobile end-device is in communication with the infrastructure device via DSRC, and the infrastructure device transmits a derived global position to the mobile end-device unable to receive a GPS signal.

Abstract: A scintillator panel that converts radiation into scintillation light includes a substrate that includes a principal surface, a scintillator layer that is disposed on the principal surface, and a reflective layer that is disposed on the scintillator layer and reflects the scintillation light. The scintillator layer includes a plurality of scintillator portions which are arranged with a predetermined pitch on the principal surface. Each scintillator portion includes a side face that extends in a direction crossing the principal surface. The reflective layer includes a plurality of metal particles with a foil shape extending along the side faces and is disposed so as to cover the side faces.

Abstract: The present invention relates to a 10B enriched plastic scintillators, methods of making the same and methods of using the same. Neither carboranes nor 3He are required to be included in the plastic scintillators, which can be used in neutron detection.

Abstract: A computer-implemented method is described for automated seismic interpretation that includes receiving, at one or more processors, a pre-stack seismic dataset representative of the subsurface volume of interest; performing, via the one or more processors, a machine learning algorithm on the pre-stack seismic dataset to identify seismic facies based on AVA clusters, wherein the identified seismic facies include cluster sequences in depth for a plurality of spatial x-y locations in the subsurface volume; performing, via the one or more processors, seismic interpretation of the seismic dataset based on the identified seismic facies to generate a digital image of the seismic interpretation; and displaying the digital image of the seismic interpretation on a user interface.

Abstract: A method and device of identifying a fracture are provided in the embodiments of the present application. The method comprises: determining three components of structure quantification for each data point in a seismic data volume; constructing a structure quantification matrix of the data point according to the three components of structure quantification for each of the data points; determining feature value and feature vector of the structure quantification matrix of each of the data points; determining fracture attribute value of the data point according to the feature value and feature vector of the structure quantification matrix of each of the data points; constructing a data volume of the fracture attribute according to the fracture attribute values of respective data points; and performing a fracture extraction for the data volume of the fracture attribute according to the feature vectors of the structure quantification matrix of the respective data points.

Abstract: A system and method are provided for creating interior seismic data between measurements of actual seismic data. The interior seismic data may be created using processes for approximating or constructing seismic data between times the actual seismic data is sampled. In some aspects, the interior seismic data may be approximated by determining a rate of change in the seismic data between at least two measurements of seismic data over time. In other aspects, the interior seismic data may be created by constructing an intermediate state of the formation between the times corresponding to at least two measurements of the seismic data based on a trend associated with the measurements. In additional aspects, a Gaussian white noise may be applied to the measurements to yield an array of equally probable predictions for the intermediate state of the property.

Abstract: Detection of contained metal contained in an article can be carried out with a high sensitivity with a simple operation in a limited space. A transmission coil 42 that generates a magnetic field for inspection from an upper surface side through a lower surface side of a placing table 21 and a plurality of magnetic sensors 43 for detecting the magnetic field are provided in a head 40 disposed on a lower surface side of the placing table 21 for placing an article which is an inspection object. When the head 40 is scanned so as to cover the entire lower surface-side region of the placing table 21, metal being contained in the article placed on the placing table 21 is detected on the basis of a change in the magnetic field being detected by the magnetic sensors 43.

Abstract: A high-Q human-portable, battery-powered self-correcting tunable transmitter apparatus for inducing alternating currents in buried conductors to facilitate their location is disclosed.

Abstract: An airborne electromagnetic survey system for geophysical prospecting comprising: a frame with a frame front section opposite a frame tail section, the frame configured to be lifted and towed by an aircraft via a tow arrangement during survey operation, the frame configured to support a transmitter coil configured to transmit an magnetic moment, wherein the frame comprises multiple frame segments, at least one of the frame segments comprising a first connection and a second connection for connecting to another one of the frame segments, a structural support providing a rigid structure between the first and second connections, and a frame segment surface providing the frame segment with an aerodynamic profile, wherein the aerodynamic profile is configured to provide aerodynamic properties to the frame, and wherein when the frame is towed by the aircraft, the frame has substantially a fixed frame shape and is substantially in a fixed operational orientation.

Abstract: A method for performing dual mode imaging of a borehole determines a reference point in a geological formation in response to a resistivity measurement of the formation. The reference point is associated with a feature, such as a fracture, in the formation. A tilt angle of the feature is determined, with respect to the reference point, in response to the received electromagnetic signals from the formation. For example a time-of-flight, ranging operation may be performed or an attenuation and phase change of the received signals may be determined to image the feature.

Abstract: A magnetic sensor for borehole magnetometer includes an upper-opened pipe-shaped housing; a frame installed at an inside of the housing; an upper-opened magnetic sensor part installed at a bottom side of the frame; a lid covering the opened upper side of the magnetic sensor part; and a magnetic sensor disposed at an inside of the magnetic sensor part to measure a magnetic force, wherein an upper side and a bottom side of the magnetic sensor is respectively installed with a spring, a bottom side of the lid and the magnetic sensor part are formed with a fixing groove for fixing an upper spring and a bottom spring each installed at an upper side and a bottom side of the magnetic sensor.

Abstract: Systems, methods, and devices for evaluation of an earth formation intersected by a borehole using a logging tool. Tools include sensor assemblies with permanent magnets mounted at a first radial distance from an axis of rotation of the sensor assembly, as well as receiver sensors. The sensor assembly is configured to generate an alternating current in a volume of interest of the formation surrounding the borehole with a time varying magnetic field in the volume produced by rotating the sensor assembly about the axis of rotation. Methods include making EM signal measurements or magnetic field measurements with receiver sensors responsive to the alternating current and estimating at least a formation property of the volume using the measurements.

Abstract: A method for making a log of material properties in a plurality of beds from an instrument utilizes steps such as estimating material properties for said plurality of beds and/or estimating positions for a plurality of bed boundaries and/or estimating orientations for said plurality of bed boundaries wherein the bed boundary orientations are individually variable. The estimated positions, orientations, and/or material properties can be utilized to compute the log.

Abstract: Embodiments of the present invention may be generally related to methods, devices, and systems which measure a gravitational field. The methods and devices may utilize an interferometer to measure tilt of a pendulum, where the tilt of the pendulum is due to a gravitational force associated with a target object. In some embodiments, the interferometer may be a displaced, even parity, Sagnac interferometer. Additionally, the interferometer may be operated in the inverse weak value domain. In some embodiments, the pendulum and interferometric readout may measure relative gravitational fields that are transverse to Earth's gravitational field. In at least some embodiments, methods and devices may have shot noise limited sensitivity sufficient to detect one kilogram 25 meters away and may have a 1 nGal resolution after mere seconds of integration. Embodiments disclosed may be used to gravitationally map density fluctuations in a target object, including the human body.

Abstract: An optoelectronic sensor for detecting objects in a monitored zone is provided that has a light transmitter having a plurality of individual light sources and a transmission optics arranged in front of the light transmitter for transmitting a transmitted light beam that is composed of a plurality of individual light beams of the individual light sources; a light receiver for generating a received signal from the transmitted light beam remitted in the monitored zone and incident on the light receiver; and an evaluation unit for detecting the objects from the received signal. An optical deflection element is arranged between the light transmitter and the transmission optics and has microoptical zones which are associated with the individual light sources and which deflect the individual light beams onto one another such that the cross-sections of the individual light beams together take up a smaller area in a virtual image plane in front of the transmission optics than the individual light sources themselves.

Abstract: The present disclosure relates to a method of calculating the radiogenic heat production (RHP) of a geophysical structure, wherein there is provided at least one geophysical parameter of the geophysical structure, the method including inverting the at least one geophysical parameter to estimate the RHP of the geophysical structure.

Abstract: A remote location monitoring system, for example, a home monitoring or weather monitoring system may include one or more sensors and/or receivers at a first location such as a residence or business to be monitored. The sensors and receivers may communicate with a remote central server via a gateway device and the detection data received from the sensors and receivers may be displayed via display circuitry coupled to a processor of the gateway device. The sensors, receivers, and gateway device may be controlled by users locally or remotely via the server. Users may register to receive remote notifications of weather events and other home monitoring events. Users may also access remotely sensors and receivers to configure alerts, notifications, and automatic responses for the devices and integrated appliances at the first location.

Abstract: The invention provides a composition comprising a three-dimensional amorphous trivalent network which reduces the number of modes within a particular frequency range (?c±??). The invention also extends to use of the composition as a structural colouration material and a paint, dye or fabric comprising the structural colouration material. Additionally, the invention extends to use of the composition as an optical filter or as a supporting matrix configured to define at least one optical component, such as a frequency filter, light-guiding structure for a telecommunications application, an optical computer chip, an optical micro-circuit or a laser comprising the supporting matrix.

Abstract: The method for producing an optical member of the present invention includes: a step (1) of applying a lower layer resin and an upper layer resin; a step (2) of pressing a die against the lower layer resin and the upper layer resin from the upper layer resin side, so as to form a resin layer including an uneven structure on a surface thereof; and a step (3) of curing the resin layer to form the polymer layer, wherein the lower layer resin contains an amide group, the lower layer resin has an amide group concentration of 1.5 mmol/g or more and less than 5 mmol/g, and the polymer layer has a minimum storage modulus E? of 1×108 Pa or higher and 1×109 Pa or lower at a bottom temperature of 110° C. or higher and 210° C. or lower.

Abstract: Methods of processing coated articles, such as transparencies, are provided comprising flash annealing one or more layers of the coated article. The one or more layers may be reflective metallic layers, such as silver layers, or comprise a transparent conductive oxide, such as indium tin oxide, or a semiconductor.

Abstract: An optical element having a substrate and a light-shielding film on part of an outer portion of the substrate further contains a coating on the light-shielding film, the coating containing a cured mixture of a melamine or benzoguanamine resin, and a phenolic resin, in proportions by mass of 1:5 to 7:5.

Abstract: Provided are a Fourier lens, a method for designing a Fourier lens, and a schlieren apparatus. The Fourier lens includes a substrate and a plurality of cuboid waveguides. The plurality of waveguides are arranged on the substrate in parallel and spaced from each other at a preset interval. The material of the substrate and the material of the waveguides are all transparent to the working waveband of the Fourier lens. The preset interval is smaller than a quotient obtained by dividing a center wavelength of the working waveband by the refractive index of the substrate. The waveguide has a plurality of widths, and the waveguides of different widths correspond to different phase delays. The individual waveguides are arranged on the substrate according to phase delays required at different positions. According to the embodiments, the range of the working angle of the Fourier lens can be increased.

Abstract: A method for fabricating an optical element including selecting a lamp spectrum and bandpass filter spectrum, obtaining a spectral characteristics vector to quantify the concentration of a component in a sample and obtaining a target spectrum from the lamp spectrum, the bandpass filter spectrum, and the spectral characteristics vector, is provided. Further including selecting a number of layers less than a maximum value, and performing an optimization routine using the index of refraction and thickness of each of the number of layers until an error between a model spectrum and the target spectrum is less than a tolerance value, or a number of iterations is exceeded. And reducing the number of layers if the error is less than a tolerance and stopping the procedure if the number of iterations is exceeded. A device using an optical element for optically-based chemometrics applications fabricated using the method above is also provided.

Abstract: A camera device includes a plurality of lenses and an annular body. The annular body is disposed between the object side and the plurality of lenses, between the plurality of lenses, or between the plurality of lenses and the image side. The annular body includes an annular main body, an outer circumferential portion, and an inner circumferential portion, wherein the annular main body connects to the outer circumferential portion and the inner circumferential portion, the annular main body is disposed between the outer circumferential portion and the inner circumferential portion, and the inner circumferential portion is non-circular and surrounds the optical axis to form a hole. The camera device satisfies: Dx>Dy, 1<Dx/Dy<28, where Dx is a maximum dimension of the hole through which the optical axis passes, and Dy is a minimum dimension of the hole through which the optical axis passes.

Abstract: A method and an apparatus for providing a matte affect while enhancing an output of a display that comprises multiple display pixels, the apparatus may include a first array of microlenses that is configured to scatter ambient light; a second array of microlenses; wherein first array of microlenses is parallel to the second array of microlenses; wherein microlenses of the first array of microlenses and the microlenses of the second array have a dimension of tens of microns; and wherein the first array of microlenses and the second array of microlenses are shaped and positioned to pass through the image from the display, when the apparatus is attached to the display.

Abstract: There is provided a diffraction optical element which comprises a base material, and in which a first resin layer having a diffraction grating shape and a second resin layer are laminated on the base material. The diffraction grating shape forms a plurality of concentric annular sections when planarly viewed from a lamination direction of the diffraction optical element. The second resin layer comprises a first portion and a second portion, and the first portion is provided on a first annular section of the first resin layer. The second portion is continuously provided from above the first portion to above a region including a periphery of the first resin layer. A difference between a refractive index of the second portion on a center of the first annular section and a refractive index of the second portion on a circumference of the first annular section is within 0.0005.

Abstract: An optical element formed of a plurality of materials includes a middle layer between a base material and a reflecting member so as to suppress stripping, cracking and the like of the optical surface due to the difference in coefficients of thermal expansion among the component materials, in the case where a temperature difference in the service environment or a temperature difference between a manufacturing environment and the service environment is large.

Abstract: Configurations are disclosed for presenting virtual reality and augmented reality experiences to users. The system may comprise a lens assembly comprising two transmissive plates, a first of the two transmissive plates comprising a first surface sag based at least in part on a cubic function, and a DOE to direct image information to a user's eye; wherein the DOE is placed in between the two transmissive plates of the lens assembly, and wherein the DOE is encoded with the inverse of the cubic function corresponding to the surface sag of the first transmissive plate; such that a wavefront created by the encoded DOE is compensated by the wavefront created by the first transmissive plate, thereby collimating light rays associated with virtual content delivered to the DOE.